Question

Can you help me solve these problems

Answer 1

2) I agree with your first step: assigning a variable to Miss B's age. Let's specifically say that this is her age in the present.

In 12 years, her age will be 12 more than in the present, or $x+12$. And this is the same as three times her age 32 years ago. So, her age 32 years ago was 32 less than in the present, so $x-32$, and we know it's three times this, so $3(x-32)$.

Now, we can write an equation and solve for x

$x+12=3(x-32)\\x+12=3x-96\\12=2x-96\\108=2x\\54=x$.

Thus, Ms. B is 54 years old now.

3) Your intuition for finding the LCD is correct; to add fractions, we need like denominators. But remember that the LCD is the least common multiple of the denominators. Using the simplest method for finding this (listing multiples), we have 4, 8, 12, 16, 20, 24, 28, ... and 6, 12, 18, 24, 30, ... and 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, .... Of these, the lowest common number is 24.

So we want to use 24 as our LCD.

$\dfrac{18x+4x+4}{24}= \dfrac{72-12x}{24}$

We can multiply both sides of the equation by 24 and then solve for x.

$18x+4x+4=72-12x\\18x+4x+12x=72-4\\34x=68\\x=2$

It's often a good idea to check your work. Plugging in 2 for x in the original equation, we see that 2 = 2.